LMFDB - Embedded newform 384.7.l.a.31.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,7,Mod(31,384)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("384.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	384.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$88.3407681100$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.9
Character	$\chi$	$=$	384.31
Dual form			384.7.l.a.223.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0227 - 11.0227i) q^{3} +(95.7535 + 95.7535i) q^{5} -338.697 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(-11.0227 - 11.0227i) q^{3} +(95.7535 + 95.7535i) q^{5} -338.697 q^{7} +243.000i q^{9} +(-1594.02 + 1594.02i) q^{11} +(-602.697 + 602.697i) q^{13} -2110.92i q^{15} -1410.09 q^{17} +(-6642.31 - 6642.31i) q^{19} +(3733.36 + 3733.36i) q^{21} -14966.5 q^{23} +2712.47i q^{25} +(2678.52 - 2678.52i) q^{27} +(25687.3 - 25687.3i) q^{29} +52243.3i q^{31} +35140.9 q^{33} +(-32431.4 - 32431.4i) q^{35} +(11201.3 + 11201.3i) q^{37} +13286.7 q^{39} -78047.4i q^{41} +(62949.8 - 62949.8i) q^{43} +(-23268.1 + 23268.1i) q^{45} +59196.3i q^{47} -2933.21 q^{49} +(15543.0 + 15543.0i) q^{51} +(45616.2 + 45616.2i) q^{53} -305266. q^{55} +146432. i q^{57} +(40115.2 - 40115.2i) q^{59} +(68015.9 - 68015.9i) q^{61} -82303.4i q^{63} -115421. q^{65} +(75821.1 + 75821.1i) q^{67} +(164972. + 164972. i) q^{69} +520740. q^{71} +349935. i q^{73} +(29898.7 - 29898.7i) q^{75} +(539891. - 539891. i) q^{77} +584164. i q^{79} -59049.0 q^{81} +(-75532.5 - 75532.5i) q^{83} +(-135021. - 135021. i) q^{85} -566286. q^{87} +881047. i q^{89} +(204132. - 204132. i) q^{91} +(575863. - 575863. i) q^{93} -1.27205e6i q^{95} +463594. q^{97} +(-387347. - 387347. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 2720 q^{11} - 3936 q^{19} - 26240 q^{23} - 66400 q^{29} + 162336 q^{35} + 7200 q^{37} + 340704 q^{43} + 806736 q^{49} + 80352 q^{51} - 443680 q^{53} - 232704 q^{55} - 886144 q^{59} + 326496 q^{61} - 372832 q^{65} - 962112 q^{67} - 541728 q^{69} - 534016 q^{71} - 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} - 2497760 q^{83} + 372000 q^{85} + 775008 q^{91} - 660960 q^{99}+O(q^{100}) $ 48 * q - 2720 * q^11 - 3936 * q^19 - 26240 * q^23 - 66400 * q^29 + 162336 * q^35 + 7200 * q^37 + 340704 * q^43 + 806736 * q^49 + 80352 * q^51 - 443680 * q^53 - 232704 * q^55 - 886144 * q^59 + 326496 * q^61 - 372832 * q^65 - 962112 * q^67 - 541728 * q^69 - 534016 * q^71 - 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 - 2497760 * q^83 + 372000 * q^85 + 775008 * q^91 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−11.0227	−	11.0227i	−0.408248	−	0.408248i
$3$	−11.0227	−	11.0227i	−0.408248	−	0.408248i
$4$		0			0
$5$	95.7535	+	95.7535i	0.766028	+	0.766028i	0.977405	−	0.211377i	$-0.0677947\pi$
$5$	95.7535	+	95.7535i	0.766028	+	0.766028i	−0.211377	+	0.977405i	$0.567795\pi$
$6$		0			0
$7$	−338.697			−0.987455			−0.493728	−	0.869617i	$-0.664366\pi$
$7$	−338.697			−0.987455			−0.493728	+	0.869617i	$0.664366\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	−1594.02	+	1594.02i	−1.19761	+	1.19761i	−0.222733	+	0.974879i	$0.571498\pi$
$11$	−1594.02	+	1594.02i	−1.19761	+	1.19761i	−0.974879	+	0.222733i	$0.928502\pi$
$12$		0			0
$13$	−602.697	+	602.697i	−0.274327	+	0.274327i	−0.830839	−	0.556512i	$-0.812139\pi$
$13$	−602.697	+	602.697i	−0.274327	+	0.274327i	0.556512	+	0.830839i	$0.312139\pi$
$14$		0			0
$15$		−	2110.92i		−	0.625459i
$16$		0			0
$17$	−1410.09			−0.287011			−0.143506	−	0.989650i	$-0.545838\pi$
$17$	−1410.09			−0.287011			−0.143506	+	0.989650i	$0.545838\pi$
$18$		0			0
$19$	−6642.31	−	6642.31i	−0.968408	−	0.968408i	0.0311079	−	0.999516i	$-0.490096\pi$
$19$	−6642.31	−	6642.31i	−0.968408	−	0.968408i	−0.999516	+	0.0311079i	$0.990096\pi$
$20$		0			0
$21$	3733.36	+	3733.36i	0.403127	+	0.403127i
$22$		0			0
$23$	−14966.5			−1.23009			−0.615046	−	0.788491i	$-0.710863\pi$
$23$	−14966.5			−1.23009			−0.615046	+	0.788491i	$0.710863\pi$
$24$		0			0
$25$			2712.47i			0.173598i
$26$		0			0
$27$	2678.52	−	2678.52i	0.136083	−	0.136083i
$28$		0			0
$29$	25687.3	−	25687.3i	1.05323	−	1.05323i	0.0547301	−	0.998501i	$-0.482570\pi$
$29$	25687.3	−	25687.3i	1.05323	−	1.05323i	0.998501	−	0.0547301i	$-0.0174298\pi$
$30$		0			0
$31$			52243.3i			1.75366i	0.480799	+	0.876831i	$0.340347\pi$
$31$			52243.3i			1.75366i	−0.480799	+	0.876831i	$0.659653\pi$
$32$		0			0
$33$	35140.9			0.977847
$34$		0			0
$35$	−32431.4	−	32431.4i	−0.756418	−	0.756418i
$36$		0			0
$37$	11201.3	+	11201.3i	0.221138	+	0.221138i	0.808977	−	0.587840i	$-0.200021\pi$
$37$	11201.3	+	11201.3i	0.221138	+	0.221138i	−0.587840	+	0.808977i	$0.700021\pi$
$38$		0			0
$39$	13286.7			0.223987
$40$		0			0
$41$		−	78047.4i		−	1.13242i	−0.824261	−	0.566209i	$-0.808409\pi$
$41$		−	78047.4i		−	1.13242i	0.824261	−	0.566209i	$-0.191591\pi$
$42$		0			0
$43$	62949.8	−	62949.8i	0.791751	−	0.791751i	−0.190027	−	0.981779i	$-0.560858\pi$
$43$	62949.8	−	62949.8i	0.791751	−	0.791751i	0.981779	+	0.190027i	$0.0608577\pi$
$44$		0			0
$45$	−23268.1	+	23268.1i	−0.255343	+	0.255343i
$46$		0			0
$47$			59196.3i			0.570166i	0.958503	+	0.285083i	$0.0920211\pi$
$47$			59196.3i			0.570166i	−0.958503	+	0.285083i	$0.907979\pi$
$48$		0			0
$49$	−2933.21			−0.0249319
$50$		0			0
$51$	15543.0	+	15543.0i	0.117172	+	0.117172i
$52$		0			0
$53$	45616.2	+	45616.2i	0.306402	+	0.306402i	0.843512	−	0.537110i	$-0.180484\pi$
$53$	45616.2	+	45616.2i	0.306402	+	0.306402i	−0.537110	+	0.843512i	$0.680484\pi$
$54$		0			0
$55$	−305266.			−1.83481
$56$		0			0
$57$			146432.i			0.790702i
$58$		0			0
$59$	40115.2	−	40115.2i	0.195323	−	0.195323i	−0.602669	−	0.797992i	$-0.705896\pi$
$59$	40115.2	−	40115.2i	0.195323	−	0.195323i	0.797992	+	0.602669i	$0.205896\pi$
$60$		0			0
$61$	68015.9	−	68015.9i	0.299654	−	0.299654i	−0.541224	−	0.840878i	$-0.682039\pi$
$61$	68015.9	−	68015.9i	0.299654	−	0.299654i	0.840878	+	0.541224i	$0.182039\pi$
$62$		0			0
$63$		−	82303.4i		−	0.329152i
$64$		0			0
$65$	−115421.			−0.420285
$66$		0			0
$67$	75821.1	+	75821.1i	0.252096	+	0.252096i	0.821829	−	0.569734i	$-0.192954\pi$
$67$	75821.1	+	75821.1i	0.252096	+	0.252096i	−0.569734	+	0.821829i	$0.692954\pi$
$68$		0			0
$69$	164972.	+	164972.i	0.502183	+	0.502183i
$70$		0			0
$71$	520740.			1.45494			0.727472	−	0.686137i	$-0.240695\pi$
$71$	520740.			1.45494			0.727472	+	0.686137i	$0.240695\pi$
$72$		0			0
$73$			349935.i			0.899537i	0.893145	+	0.449768i	$0.148494\pi$
$73$			349935.i			0.899537i	−0.893145	+	0.449768i	$0.851506\pi$
$74$		0			0
$75$	29898.7	−	29898.7i	0.0708710	−	0.0708710i
$76$		0			0
$77$	539891.	−	539891.i	1.18259	−	1.18259i
$78$		0			0
$79$			584164.i			1.18482i	0.805635	+	0.592412i	$0.201824\pi$
$79$			584164.i			1.18482i	−0.805635	+	0.592412i	$0.798176\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	−75532.5	−	75532.5i	−0.132099	−	0.132099i	0.637966	−	0.770065i	$-0.279776\pi$
$83$	−75532.5	−	75532.5i	−0.132099	−	0.132099i	−0.770065	+	0.637966i	$0.779776\pi$
$84$		0			0
$85$	−135021.	−	135021.i	−0.219859	−	0.219859i
$86$		0			0
$87$	−566286.			−0.859960
$88$		0			0
$89$			881047.i			1.24977i	0.780718	+	0.624884i	$0.214854\pi$
$89$			881047.i			1.24977i	−0.780718	+	0.624884i	$0.785146\pi$
$90$		0			0
$91$	204132.	−	204132.i	0.270886	−	0.270886i
$92$		0			0
$93$	575863.	−	575863.i	0.715929	−	0.715929i
$94$		0			0
$95$		−	1.27205e6i		−	1.48366i
$96$		0			0
$97$	463594.			0.507952			0.253976	−	0.967211i	$-0.418262\pi$
$97$	463594.			0.507952			0.253976	+	0.967211i	$0.418262\pi$
$98$		0			0
$99$	−387347.	−	387347.i	−0.399204	−	0.399204i
$100$		0			0
$101$	−457625.	−	457625.i	−0.444166	−	0.444166i	0.449243	−	0.893409i	$-0.351694\pi$
$101$	−457625.	−	457625.i	−0.444166	−	0.444166i	−0.893409	+	0.449243i	$0.851694\pi$
$102$		0			0
$103$	−1.49249e6			−1.36584			−0.682921	−	0.730492i	$-0.739291\pi$
$103$	−1.49249e6			−1.36584			−0.682921	+	0.730492i	$0.739291\pi$
$104$		0			0
$105$			714964.i			0.617613i
$106$		0			0
$107$	1.61763e6	−	1.61763e6i	1.32047	−	1.32047i	0.407072	−	0.913396i	$-0.366550\pi$
$107$	1.61763e6	−	1.61763e6i	1.32047	−	1.32047i	0.913396	−	0.407072i	$-0.133450\pi$
$108$		0			0
$109$	212604.	−	212604.i	0.164170	−	0.164170i	−0.620241	−	0.784411i	$-0.712965\pi$
$109$	212604.	−	212604.i	0.164170	−	0.164170i	0.784411	+	0.620241i	$0.212965\pi$
$110$		0			0
$111$		−	246937.i		−	0.180558i
$112$		0			0
$113$	1.23333e6			0.854760			0.427380	−	0.904072i	$-0.359437\pi$
$113$	1.23333e6			0.854760			0.427380	+	0.904072i	$0.359437\pi$
$114$		0			0
$115$	−1.43310e6	−	1.43310e6i	−0.942285	−	0.942285i
$116$		0			0
$117$	−146455.	−	146455.i	−0.0914425	−	0.0914425i
$118$		0			0
$119$	477592.			0.283411
$120$		0			0
$121$		−	3.31025e6i		−	1.86855i
$122$		0			0
$123$	−860294.	+	860294.i	−0.462308	+	0.462308i
$124$		0			0
$125$	1.23642e6	−	1.23642e6i	0.633047	−	0.633047i
$126$		0			0
$127$		−	2.86669e6i		−	1.39949i	−0.714394	−	0.699744i	$-0.753297\pi$
$127$		−	2.86669e6i		−	1.39949i	0.714394	−	0.699744i	$-0.246703\pi$
$128$		0			0
$129$	−1.38775e6			−0.646462
$130$		0			0
$131$	−1.18710e6	−	1.18710e6i	−0.528046	−	0.528046i	0.391943	−	0.919989i	$-0.371803\pi$
$131$	−1.18710e6	−	1.18710e6i	−0.528046	−	0.528046i	−0.919989	+	0.391943i	$0.871803\pi$
$132$		0			0
$133$	2.24973e6	+	2.24973e6i	0.956260	+	0.956260i
$134$		0			0
$135$	512955.			0.208486
$136$		0			0
$137$		−	4.54167e6i		−	1.76626i	−0.469132	−	0.883128i	$-0.655433\pi$
$137$		−	4.54167e6i		−	1.76626i	0.469132	−	0.883128i	$-0.344567\pi$
$138$		0			0
$139$	3.47603e6	−	3.47603e6i	1.29431	−	1.29431i	0.362218	−	0.932093i	$-0.382020\pi$
$139$	3.47603e6	−	3.47603e6i	1.29431	−	1.29431i	0.932093	−	0.362218i	$-0.117980\pi$
$140$		0			0
$141$	652504.	−	652504.i	0.232769	−	0.232769i
$142$		0			0
$143$		−	1.92143e6i		−	0.657076i
$144$		0			0
$145$	4.91929e6			1.61361
$146$		0			0
$147$	32331.9	+	32331.9i	0.0101784	+	0.0101784i
$148$		0			0
$149$	−1.14413e6	−	1.14413e6i	−0.345873	−	0.345873i	0.512697	−	0.858570i	$-0.328646\pi$
$149$	−1.14413e6	−	1.14413e6i	−0.345873	−	0.345873i	−0.858570	+	0.512697i	$0.828646\pi$
$150$		0			0
$151$	2.06680e6			0.600300			0.300150	−	0.953892i	$-0.402963\pi$
$151$	2.06680e6			0.600300			0.300150	+	0.953892i	$0.402963\pi$
$152$		0			0
$153$		−	342651.i		−	0.0956704i
$154$		0			0
$155$	−5.00248e6	+	5.00248e6i	−1.34335	+	1.34335i
$156$		0			0
$157$	994443.	−	994443.i	0.256969	−	0.256969i	−0.566851	−	0.823820i	$-0.691839\pi$
$157$	994443.	−	994443.i	0.256969	−	0.256969i	0.823820	+	0.566851i	$0.191839\pi$
$158$		0			0
$159$		−	1.00563e6i		−	0.250176i
$160$		0			0
$161$	5.06912e6			1.21466
$162$		0			0
$163$	−477011.	−	477011.i	−0.110145	−	0.110145i	0.649886	−	0.760032i	$-0.274817\pi$
$163$	−477011.	−	477011.i	−0.110145	−	0.110145i	−0.760032	+	0.649886i	$0.774817\pi$
$164$		0			0
$165$	3.36486e6	+	3.36486e6i	0.749058	+	0.749058i
$166$		0			0
$167$	−566969.			−0.121733			−0.0608667	−	0.998146i	$-0.519386\pi$
$167$	−566969.			−0.121733			−0.0608667	+	0.998146i	$0.519386\pi$
$168$		0			0
$169$			4.10032e6i			0.849489i
$170$		0			0
$171$	1.61408e6	−	1.61408e6i	0.322803	−	0.322803i
$172$		0			0
$173$	−6.06937e6	+	6.06937e6i	−1.17221	+	1.17221i	−0.190528	+	0.981682i	$0.561020\pi$
$173$	−6.06937e6	+	6.06937e6i	−1.17221	+	1.17221i	−0.981682	+	0.190528i	$0.938980\pi$
$174$		0			0
$175$		−	918705.i		−	0.171420i
$176$		0			0
$177$	−884356.			−0.159480
$178$		0			0
$179$	−6.12901e6	−	6.12901e6i	−1.06864	−	1.06864i	−0.997464	−	0.0711761i	$-0.977325\pi$
$179$	−6.12901e6	−	6.12901e6i	−1.06864	−	1.06864i	−0.0711761	−	0.997464i	$-0.522675\pi$
$180$		0			0
$181$	3.73717e6	+	3.73717e6i	0.630242	+	0.630242i	0.948129	−	0.317886i	$-0.102973\pi$
$181$	3.73717e6	+	3.73717e6i	0.630242	+	0.630242i	−0.317886	+	0.948129i	$0.602973\pi$
$182$		0			0
$183$	−1.49944e6			−0.244667
$184$		0			0
$185$			2.14512e6i			0.338795i
$186$		0			0
$187$	2.24771e6	−	2.24771e6i	0.343728	−	0.343728i
$188$		0			0
$189$	−907206.	+	907206.i	−0.134376	+	0.134376i
$190$		0			0
$191$		−	7.48444e6i		−	1.07414i	−0.843539	−	0.537068i	$-0.819532\pi$
$191$		−	7.48444e6i		−	1.07414i	0.843539	−	0.537068i	$-0.180468\pi$
$192$		0			0
$193$	1.84618e6			0.256804			0.128402	−	0.991722i	$-0.459015\pi$
$193$	1.84618e6			0.256804			0.128402	+	0.991722i	$0.459015\pi$
$194$		0			0
$195$	1.27225e6	+	1.27225e6i	0.171581	+	0.171581i
$196$		0			0
$197$	5.01650e6	+	5.01650e6i	0.656149	+	0.656149i	0.954467	−	0.298318i	$-0.0964255\pi$
$197$	5.01650e6	+	5.01650e6i	0.656149	+	0.656149i	−0.298318	+	0.954467i	$0.596425\pi$
$198$		0			0
$199$	−3.90212e6			−0.495155			−0.247578	−	0.968868i	$-0.579635\pi$
$199$	−3.90212e6			−0.495155			−0.247578	+	0.968868i	$0.579635\pi$
$200$		0			0
$201$		−	1.67151e6i		−	0.205835i
$202$		0			0
$203$	−8.70020e6	+	8.70020e6i	−1.04002	+	1.04002i
$204$		0			0
$205$	7.47331e6	−	7.47331e6i	0.867464	−	0.867464i
$206$		0			0
$207$		−	3.63687e6i		−	0.410031i
$208$		0			0
$209$	2.11760e7			2.31956
$210$		0			0
$211$	9.10818e6	+	9.10818e6i	0.969581	+	0.969581i	0.999551	−	0.0299699i	$-0.00954116\pi$
$211$	9.10818e6	+	9.10818e6i	0.969581	+	0.969581i	−0.0299699	+	0.999551i	$0.509541\pi$
$212$		0			0
$213$	−5.73997e6	−	5.73997e6i	−0.593978	−	0.593978i
$214$		0			0
$215$	1.20553e7			1.21301
$216$		0			0
$217$		−	1.76947e7i		−	1.73166i
$218$		0			0
$219$	3.85723e6	−	3.85723e6i	0.367234	−	0.367234i
$220$		0			0
$221$	849855.	−	849855.i	0.0787350	−	0.0787350i
$222$		0			0
$223$		−	3.47876e6i		−	0.313697i	−0.987623	−	0.156848i	$-0.949867\pi$
$223$		−	3.47876e6i		−	0.313697i	0.987623	−	0.156848i	$-0.0501334\pi$
$224$		0			0
$225$	−659129.			−0.0578660
$226$		0			0
$227$	−8.39488e6	−	8.39488e6i	−0.717690	−	0.717690i	0.250441	−	0.968132i	$-0.419424\pi$
$227$	−8.39488e6	−	8.39488e6i	−0.717690	−	0.717690i	−0.968132	+	0.250441i	$0.919424\pi$
$228$		0			0
$229$	−9.40100e6	−	9.40100e6i	−0.782830	−	0.782830i	0.197477	−	0.980308i	$-0.436725\pi$
$229$	−9.40100e6	−	9.40100e6i	−0.782830	−	0.782830i	−0.980308	+	0.197477i	$0.936725\pi$
$230$		0			0
$231$	−1.19021e7			−0.965580
$232$		0			0
$233$			1.24039e7i			0.980599i	0.871554	+	0.490299i	$0.163113\pi$
$233$			1.24039e7i			0.980599i	−0.871554	+	0.490299i	$0.836887\pi$
$234$		0			0
$235$	−5.66826e6	+	5.66826e6i	−0.436763	+	0.436763i
$236$		0			0
$237$	6.43907e6	−	6.43907e6i	0.483702	−	0.483702i
$238$		0			0
$239$		−	3.38975e6i		−	0.248299i	−0.992264	−	0.124149i	$-0.960380\pi$
$239$		−	3.38975e6i		−	0.248299i	0.992264	−	0.124149i	$-0.0396202\pi$
$240$		0			0
$241$	−7.75493e6			−0.554022			−0.277011	−	0.960867i	$-0.589344\pi$
$241$	−7.75493e6			−0.554022			−0.277011	+	0.960867i	$0.589344\pi$
$242$		0			0
$243$	650880.	+	650880.i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−280865.	−	280865.i	−0.0190985	−	0.0190985i
$246$		0			0
$247$	8.00660e6			0.531322
$248$		0			0
$249$			1.66515e6i			0.107858i
$250$		0			0
$251$	6.71306e6	−	6.71306e6i	0.424521	−	0.424521i	−0.462236	−	0.886757i	$-0.652953\pi$
$251$	6.71306e6	−	6.71306e6i	0.424521	−	0.424521i	0.886757	+	0.462236i	$0.152953\pi$
$252$		0			0
$253$	2.38570e7	−	2.38570e7i	1.47317	−	1.47317i
$254$		0			0
$255$			2.97659e6i			0.179514i
$256$		0			0
$257$	−1.78180e7			−1.04969			−0.524844	−	0.851198i	$-0.675876\pi$
$257$	−1.78180e7			−1.04969			−0.524844	+	0.851198i	$0.675876\pi$
$258$		0			0
$259$	−3.79384e6	−	3.79384e6i	−0.218364	−	0.218364i
$260$		0			0
$261$	6.24200e6	+	6.24200e6i	0.351077	+	0.351077i
$262$		0			0
$263$	−1.27225e7			−0.699365			−0.349683	−	0.936868i	$-0.613711\pi$
$263$	−1.27225e7			−0.699365			−0.349683	+	0.936868i	$0.613711\pi$
$264$		0			0
$265$			8.73583e6i			0.469425i
$266$		0			0
$267$	9.71152e6	−	9.71152e6i	0.510215	−	0.510215i
$268$		0			0
$269$	−1.77250e7	+	1.77250e7i	−0.910604	+	0.910604i	−0.996320	−	0.0857153i	$-0.972682\pi$
$269$	−1.77250e7	+	1.77250e7i	−0.910604	+	0.910604i	0.0857153	+	0.996320i	$0.472682\pi$
$270$		0			0
$271$		−	4.03947e6i		−	0.202963i	−0.994837	−	0.101481i	$-0.967642\pi$
$271$		−	4.03947e6i		−	0.202963i	0.994837	−	0.101481i	$-0.0323582\pi$
$272$		0			0
$273$	−4.50017e6			−0.221178
$274$		0			0
$275$	−4.32373e6	−	4.32373e6i	−0.207903	−	0.207903i
$276$		0			0
$277$	−2.71660e6	−	2.71660e6i	−0.127816	−	0.127816i	0.640305	−	0.768121i	$-0.278808\pi$
$277$	−2.71660e6	−	2.71660e6i	−0.127816	−	0.127816i	−0.768121	+	0.640305i	$0.778808\pi$
$278$		0			0
$279$	−1.26951e7			−0.584554
$280$		0			0
$281$			3.00632e6i			0.135493i	0.997703	+	0.0677464i	$0.0215809\pi$
$281$			3.00632e6i			0.135493i	−0.997703	+	0.0677464i	$0.978419\pi$
$282$		0			0
$283$	−7.04093e6	+	7.04093e6i	−0.310650	+	0.310650i	−0.845161	−	0.534512i	$-0.820496\pi$
$283$	−7.04093e6	+	7.04093e6i	−0.310650	+	0.310650i	0.534512	+	0.845161i	$0.320496\pi$
$284$		0			0
$285$	−1.40214e7	+	1.40214e7i	−0.605700	+	0.605700i
$286$		0			0
$287$			2.64344e7i			1.11821i
$288$		0			0
$289$	−2.21492e7			−0.917625
$290$		0			0
$291$	−5.11006e6	−	5.11006e6i	−0.207370	−	0.207370i
$292$		0			0
$293$	1.09177e6	+	1.09177e6i	0.0434037	+	0.0434037i	0.728476	−	0.685072i	$-0.240229\pi$
$293$	1.09177e6	+	1.09177e6i	0.0434037	+	0.0434037i	−0.685072	+	0.728476i	$0.740229\pi$
$294$		0			0
$295$	7.68234e6			0.299245
$296$		0			0
$297$			8.53923e6i			0.325949i
$298$		0			0
$299$	9.02029e6	−	9.02029e6i	0.337448	−	0.337448i
$300$		0			0
$301$	−2.13209e7	+	2.13209e7i	−0.781819	+	0.781819i
$302$		0			0
$303$			1.00885e7i			0.362660i
$304$		0			0
$305$	1.30255e7			0.459087
$306$		0			0
$307$	3.35575e7	+	3.35575e7i	1.15978	+	1.15978i	0.984524	+	0.175252i	$0.0560740\pi$
$307$	3.35575e7	+	3.35575e7i	1.15978	+	1.15978i	0.175252	+	0.984524i	$0.443926\pi$
$308$		0			0
$309$	1.64513e7	+	1.64513e7i	0.557603	+	0.557603i
$310$		0			0
$311$	7.25043e6			0.241036			0.120518	−	0.992711i	$-0.461544\pi$
$311$	7.25043e6			0.241036			0.120518	+	0.992711i	$0.461544\pi$
$312$		0			0
$313$		−	5.86126e6i		−	0.191143i	−0.995423	−	0.0955714i	$-0.969532\pi$
$313$		−	5.86126e6i		−	0.191143i	0.995423	−	0.0955714i	$-0.0304678\pi$
$314$		0			0
$315$	7.88084e6	−	7.88084e6i	0.252139	−	0.252139i
$316$		0			0
$317$	−1.42197e7	+	1.42197e7i	−0.446388	+	0.446388i	−0.894152	−	0.447764i	$-0.852221\pi$
$317$	−1.42197e7	+	1.42197e7i	−0.446388	+	0.446388i	0.447764	+	0.894152i	$0.352221\pi$
$318$		0			0
$319$			8.18921e7i			2.52273i
$320$		0			0
$321$	−3.56613e7			−1.07816
$322$		0			0
$323$	9.36623e6	+	9.36623e6i	0.277944	+	0.277944i
$324$		0			0
$325$	−1.63480e6	−	1.63480e6i	−0.0476226	−	0.0476226i
$326$		0			0
$327$	−4.68695e6			−0.134044
$328$		0			0
$329$		−	2.00496e7i		−	0.563013i
$330$		0			0
$331$	4.55754e7	−	4.55754e7i	1.25674	−	1.25674i	0.304106	−	0.952638i	$-0.401642\pi$
$331$	4.55754e7	−	4.55754e7i	1.25674	−	1.25674i	0.952638	−	0.304106i	$-0.0983577\pi$
$332$		0			0
$333$	−2.72191e6	+	2.72191e6i	−0.0737125	+	0.0737125i
$334$		0			0
$335$			1.45203e7i			0.386225i
$336$		0			0
$337$	−5.70761e7			−1.49130			−0.745650	−	0.666338i	$-0.767861\pi$
$337$	−5.70761e7			−1.49130			−0.745650	+	0.666338i	$0.767861\pi$
$338$		0			0
$339$	−1.35946e7	−	1.35946e7i	−0.348954	−	0.348954i
$340$		0			0
$341$	−8.32771e7	−	8.32771e7i	−2.10021	−	2.10021i
$342$		0			0
$343$	4.08409e7			1.01207
$344$		0			0
$345$			3.15932e7i			0.769373i
$346$		0			0
$347$	−1.33582e7	+	1.33582e7i	−0.319713	+	0.319713i	−0.848657	−	0.528944i	$-0.822588\pi$
$347$	−1.33582e7	+	1.33582e7i	−0.319713	+	0.319713i	0.528944	+	0.848657i	$0.322588\pi$
$348$		0			0
$349$	5.81390e7	−	5.81390e7i	1.36770	−	1.36770i	0.503993	−	0.863708i	$-0.331864\pi$
$349$	5.81390e7	−	5.81390e7i	1.36770	−	1.36770i	0.863708	−	0.503993i	$-0.168136\pi$
$350$		0			0
$351$			3.22867e6i			0.0746625i
$352$		0			0
$353$	−3.25741e7			−0.740539			−0.370269	−	0.928924i	$-0.620735\pi$
$353$	−3.25741e7			−0.740539			−0.370269	+	0.928924i	$0.620735\pi$
$354$		0			0
$355$	4.98627e7	+	4.98627e7i	1.11453	+	1.11453i
$356$		0			0
$357$	−5.26436e6	−	5.26436e6i	−0.115702	−	0.115702i
$358$		0			0
$359$	1.13980e7			0.246346			0.123173	−	0.992385i	$-0.460693\pi$
$359$	1.13980e7			0.246346			0.123173	+	0.992385i	$0.460693\pi$
$360$		0			0
$361$			4.11947e7i			0.875628i
$362$		0			0
$363$	−3.64880e7	+	3.64880e7i	−0.762833	+	0.762833i
$364$		0			0
$365$	−3.35075e7	+	3.35075e7i	−0.689071	+	0.689071i
$366$		0			0
$367$			6.66527e6i			0.134840i	0.997725	+	0.0674201i	$0.0214768\pi$
$367$			6.66527e6i			0.134840i	−0.997725	+	0.0674201i	$0.978523\pi$
$368$		0			0
$369$	1.89655e7			0.377473
$370$		0			0
$371$	−1.54501e7	−	1.54501e7i	−0.302559	−	0.302559i
$372$		0			0
$373$	3.13045e7	+	3.13045e7i	0.603226	+	0.603226i	0.941167	−	0.337941i	$-0.109731\pi$
$373$	3.13045e7	+	3.13045e7i	0.603226	+	0.603226i	−0.337941	+	0.941167i	$0.609731\pi$
$374$		0			0
$375$	−2.72574e7			−0.516881
$376$		0			0
$377$			3.09633e7i			0.577860i
$378$		0			0
$379$	−3.59578e7	+	3.59578e7i	−0.660503	+	0.660503i	−0.955499	−	0.294995i	$-0.904682\pi$
$379$	−3.59578e7	+	3.59578e7i	−0.660503	+	0.660503i	0.294995	+	0.955499i	$0.404682\pi$
$380$		0			0
$381$	−3.15986e7	+	3.15986e7i	−0.571338	+	0.571338i
$382$		0			0
$383$		−	4.29186e6i		−	0.0763923i	−0.999270	−	0.0381962i	$-0.987839\pi$
$383$		−	4.29186e6i		−	0.0763923i	0.999270	−	0.0381962i	$-0.0121612\pi$
$384$		0			0
$385$	1.03393e8			1.81179
$386$		0			0
$387$	1.52968e7	+	1.52968e7i	0.263917	+	0.263917i
$388$		0			0
$389$	2.81391e7	+	2.81391e7i	0.478037	+	0.478037i	0.904503	−	0.426467i	$-0.140242\pi$
$389$	2.81391e7	+	2.81391e7i	0.478037	+	0.478037i	−0.426467	+	0.904503i	$0.640242\pi$
$390$		0			0
$391$	2.11041e7			0.353050
$392$		0			0
$393$			2.61700e7i			0.431148i
$394$		0			0
$395$	−5.59358e7	+	5.59358e7i	−0.907608	+	0.907608i
$396$		0			0
$397$	102931.	−	102931.i	0.00164504	−	0.00164504i	−0.706284	−	0.707929i	$-0.749630\pi$
$397$	102931.	−	102931.i	0.00164504	−	0.00164504i	0.707929	+	0.706284i	$0.249630\pi$
$398$		0			0
$399$		−	4.95963e7i		−	0.780783i
$400$		0			0
$401$	−9.77419e7			−1.51582			−0.757910	−	0.652359i	$-0.773779\pi$
$401$	−9.77419e7			−1.51582			−0.757910	+	0.652359i	$0.773779\pi$
$402$		0			0
$403$	−3.14869e7	−	3.14869e7i	−0.481077	−	0.481077i
$404$		0			0
$405$	−5.65415e6	−	5.65415e6i	−0.0851142	−	0.0851142i
$406$		0			0
$407$	−3.57102e7			−0.529674
$408$		0			0
$409$		−	1.16185e8i		−	1.69817i	−0.528255	−	0.849086i	$-0.677153\pi$
$409$		−	1.16185e8i		−	1.69817i	0.528255	−	0.849086i	$-0.322847\pi$
$410$		0			0
$411$	−5.00615e7	+	5.00615e7i	−0.721071	+	0.721071i
$412$		0			0
$413$	−1.35869e7	+	1.35869e7i	−0.192873	+	0.192873i
$414$		0			0
$415$		−	1.44650e7i		−	0.202383i
$416$		0			0
$417$	−7.66304e7			−1.05680
$418$		0			0
$419$	1.00557e8	+	1.00557e8i	1.36701	+	1.36701i	0.864669	+	0.502341i	$0.167528\pi$
$419$	1.00557e8	+	1.00557e8i	1.36701	+	1.36701i	0.502341	+	0.864669i	$0.332472\pi$
$420$		0			0
$421$	−6.79990e7	−	6.79990e7i	−0.911289	−	0.911289i	0.0850844	−	0.996374i	$-0.472884\pi$
$421$	−6.79990e7	−	6.79990e7i	−0.911289	−	0.911289i	−0.996374	+	0.0850844i	$0.972884\pi$
$422$		0			0
$423$	−1.43847e7			−0.190055
$424$		0			0
$425$		−	3.82481e6i		−	0.0498245i
$426$		0			0
$427$	−2.30368e7	+	2.30368e7i	−0.295895	+	0.295895i
$428$		0			0
$429$	−2.11793e7	+	2.11793e7i	−0.268250	+	0.268250i
$430$		0			0
$431$		−	8.48038e7i		−	1.05921i	−0.848243	−	0.529607i	$-0.822340\pi$
$431$		−	8.48038e7i		−	1.05921i	0.848243	−	0.529607i	$-0.177660\pi$
$432$		0			0
$433$	1.35872e8			1.67366			0.836830	−	0.547463i	$-0.184406\pi$
$433$	1.35872e8			1.67366			0.836830	+	0.547463i	$0.184406\pi$
$434$		0			0
$435$	−5.42239e7	−	5.42239e7i	−0.658753	−	0.658753i
$436$		0			0
$437$	9.94124e7	+	9.94124e7i	1.19123	+	1.19123i
$438$		0			0
$439$	2.21120e7			0.261357			0.130679	−	0.991425i	$-0.458284\pi$
$439$	2.21120e7			0.261357			0.130679	+	0.991425i	$0.458284\pi$
$440$		0			0
$441$		−	712770.i		−	0.00831063i
$442$		0			0
$443$	−1.39108e7	+	1.39108e7i	−0.160008	+	0.160008i	−0.782570	−	0.622562i	$-0.786092\pi$
$443$	−1.39108e7	+	1.39108e7i	−0.160008	+	0.160008i	0.622562	+	0.782570i	$0.286092\pi$
$444$		0			0
$445$	−8.43634e7	+	8.43634e7i	−0.957357	+	0.957357i
$446$		0			0
$447$			2.52228e7i			0.282404i
$448$		0			0
$449$	3.72059e7			0.411029			0.205515	−	0.978654i	$-0.434113\pi$
$449$	3.72059e7			0.411029			0.205515	+	0.978654i	$0.434113\pi$
$450$		0			0
$451$	1.24409e8	+	1.24409e8i	1.35620	+	1.35620i
$452$		0			0
$453$	−2.27818e7	−	2.27818e7i	−0.245071	−	0.245071i
$454$		0			0
$455$	3.90927e7			0.415013
$456$		0			0
$457$		−	1.71918e8i		−	1.80124i	−0.434603	−	0.900622i	$-0.643111\pi$
$457$		−	1.71918e8i		−	1.80124i	0.434603	−	0.900622i	$-0.356889\pi$
$458$		0			0
$459$	−3.77694e6	+	3.77694e6i	−0.0390573	+	0.0390573i
$460$		0			0
$461$	5.67322e7	−	5.67322e7i	0.579064	−	0.579064i	−0.355581	−	0.934645i	$-0.615717\pi$
$461$	5.67322e7	−	5.67322e7i	0.579064	−	0.579064i	0.934645	+	0.355581i	$0.115717\pi$
$462$		0			0
$463$			1.56654e8i			1.57833i	0.614180	+	0.789166i	$0.289487\pi$
$463$			1.56654e8i			1.57833i	−0.614180	+	0.789166i	$0.710513\pi$
$464$		0			0
$465$	1.10282e8			1.09684
$466$		0			0
$467$	−1.11254e8	−	1.11254e8i	−1.09236	−	1.09236i	−0.995276	−	0.0970811i	$-0.969049\pi$
$467$	−1.11254e8	−	1.11254e8i	−1.09236	−	1.09236i	−0.0970811	−	0.995276i	$-0.530951\pi$
$468$		0			0
$469$	−2.56804e7	−	2.56804e7i	−0.248933	−	0.248933i
$470$		0			0
$471$	−2.19229e7			−0.209814
$472$		0			0
$473$			2.00687e8i			1.89642i
$474$		0			0
$475$	1.80170e7	−	1.80170e7i	0.168114	−	0.168114i
$476$		0			0
$477$	−1.10847e7	+	1.10847e7i	−0.102134	+	0.102134i
$478$		0			0
$479$			4.71347e7i			0.428878i	0.976737	+	0.214439i	$0.0687924\pi$
$479$			4.71347e7i			0.428878i	−0.976737	+	0.214439i	$0.931208\pi$
$480$		0			0
$481$	−1.35020e7			−0.121328
$482$		0			0
$483$	−5.58754e7	−	5.58754e7i	−0.495883	−	0.495883i
$484$		0			0
$485$	4.43907e7	+	4.43907e7i	0.389105	+	0.389105i
$486$		0			0
$487$	1.00829e8			0.872972			0.436486	−	0.899711i	$-0.356223\pi$
$487$	1.00829e8			0.872972			0.436486	+	0.899711i	$0.356223\pi$
$488$		0			0
$489$			1.05159e7i			0.0899333i
$490$		0			0
$491$	9.12387e7	−	9.12387e7i	0.770788	−	0.770788i	−0.207457	−	0.978244i	$-0.566519\pi$
$491$	9.12387e7	−	9.12387e7i	0.770788	−	0.770788i	0.978244	+	0.207457i	$0.0665185\pi$
$492$		0			0
$493$	−3.62212e7	+	3.62212e7i	−0.302289	+	0.302289i
$494$		0			0
$495$		−	7.41798e7i		−	0.611603i
$496$		0			0
$497$	−1.76373e8			−1.43669
$498$		0			0
$499$	7.61214e7	+	7.61214e7i	0.612640	+	0.612640i	0.943633	−	0.330994i	$-0.107384\pi$
$499$	7.61214e7	+	7.61214e7i	0.612640	+	0.612640i	−0.330994	+	0.943633i	$0.607384\pi$
$500$		0			0
$501$	6.24953e6	+	6.24953e6i	0.0496975	+	0.0496975i
$502$		0			0
$503$	−1.11499e8			−0.876127			−0.438063	−	0.898944i	$-0.644335\pi$
$503$	−1.11499e8			−0.876127			−0.438063	+	0.898944i	$0.644335\pi$
$504$		0			0
$505$		−	8.76383e7i		−	0.680487i
$506$		0			0
$507$	4.51966e7	−	4.51966e7i	0.346802	−	0.346802i
$508$		0			0
$509$	−7.40728e7	+	7.40728e7i	−0.561701	+	0.561701i	−0.929790	−	0.368089i	$-0.880012\pi$
$509$	−7.40728e7	+	7.40728e7i	−0.561701	+	0.561701i	0.368089	+	0.929790i	$0.380012\pi$
$510$		0			0
$511$		−	1.18522e8i		−	0.888253i
$512$		0			0
$513$	−3.55831e7			−0.263567
$514$		0			0
$515$	−1.42911e8	−	1.42911e8i	−1.04627	−	1.04627i
$516$		0			0
$517$	−9.43603e7	−	9.43603e7i	−0.682838	−	0.682838i
$518$		0			0
$519$	1.33802e8			0.957106
$520$		0			0
$521$		−	8.30371e7i		−	0.587163i	−0.955934	−	0.293582i	$-0.905153\pi$
$521$		−	8.30371e7i		−	0.587163i	0.955934	−	0.293582i	$-0.0948472\pi$
$522$		0			0
$523$	8.42929e7	−	8.42929e7i	0.589231	−	0.589231i	−0.348192	−	0.937423i	$-0.613204\pi$
$523$	8.42929e7	−	8.42929e7i	0.589231	−	0.589231i	0.937423	+	0.348192i	$0.113204\pi$
$524$		0			0
$525$	−1.01266e7	+	1.01266e7i	−0.0699820	+	0.0699820i
$526$		0			0
$527$		−	7.36676e7i		−	0.503320i
$528$		0			0
$529$	7.59612e7			0.513127
$530$		0			0
$531$	9.74799e6	+	9.74799e6i	0.0651076	+	0.0651076i
$532$		0			0
$533$	4.70390e7	+	4.70390e7i	0.310653	+	0.310653i
$534$		0			0
$535$	3.09788e8			2.02303
$536$		0			0
$537$			1.35117e8i			0.872541i
$538$		0			0
$539$	4.67561e6	−	4.67561e6i	0.0298587	−	0.0298587i
$540$		0			0
$541$	2.21061e8	−	2.21061e8i	1.39611	−	1.39611i	0.585287	−	0.810826i	$-0.300982\pi$
$541$	2.21061e8	−	2.21061e8i	1.39611	−	1.39611i	0.810826	−	0.585287i	$-0.199018\pi$
$542$		0			0
$543$		−	8.23875e7i		−	0.514591i
$544$		0			0
$545$	4.07152e7			0.251517
$546$		0			0
$547$	−1.41321e8	−	1.41321e8i	−0.863464	−	0.863464i	0.128275	−	0.991739i	$-0.459056\pi$
$547$	−1.41321e8	−	1.41321e8i	−0.863464	−	0.863464i	−0.991739	+	0.128275i	$0.959056\pi$
$548$		0			0
$549$	1.65279e7	+	1.65279e7i	0.0998848	+	0.0998848i
$550$		0			0
$551$	−3.41246e8			−2.03992
$552$		0			0
$553$		−	1.97855e8i		−	1.16996i
$554$		0			0
$555$	2.36451e7	−	2.36451e7i	0.138313	−	0.138313i
$556$		0			0
$557$	4.48748e7	−	4.48748e7i	0.259679	−	0.259679i	−0.565244	−	0.824924i	$-0.691218\pi$
$557$	4.48748e7	−	4.48748e7i	0.259679	−	0.259679i	0.824924	+	0.565244i	$0.191218\pi$
$558$		0			0
$559$			7.58793e7i			0.434398i
$560$		0			0
$561$	−4.95517e7			−0.280653
$562$		0			0
$563$	6.88093e7	+	6.88093e7i	0.385586	+	0.385586i	0.873110	−	0.487523i	$-0.162100\pi$
$563$	6.88093e7	+	6.88093e7i	0.385586	+	0.385586i	−0.487523	+	0.873110i	$0.662100\pi$
$564$		0			0
$565$	1.18096e8	+	1.18096e8i	0.654770	+	0.654770i
$566$		0			0
$567$	1.99997e7			0.109717
$568$		0			0
$569$			2.18716e7i			0.118726i	0.998236	+	0.0593628i	$0.0189069\pi$
$569$			2.18716e7i			0.118726i	−0.998236	+	0.0593628i	$0.981093\pi$
$570$		0			0
$571$	6.28910e7	−	6.28910e7i	0.337816	−	0.337816i	−0.517729	−	0.855545i	$-0.673222\pi$
$571$	6.28910e7	−	6.28910e7i	0.337816	−	0.337816i	0.855545	+	0.517729i	$0.173222\pi$
$572$		0			0
$573$	−8.24987e7	+	8.24987e7i	−0.438514	+	0.438514i
$574$		0			0
$575$		−	4.05962e7i		−	0.213541i
$576$		0			0
$577$	1.05532e8			0.549359			0.274680	−	0.961536i	$-0.411428\pi$
$577$	1.05532e8			0.549359			0.274680	+	0.961536i	$0.411428\pi$
$578$		0			0
$579$	−2.03499e7	−	2.03499e7i	−0.104840	−	0.104840i
$580$		0			0
$581$	2.55827e7	+	2.55827e7i	0.130442	+	0.130442i
$582$		0			0
$583$	−1.45427e8			−0.733902
$584$		0			0
$585$		−	2.80472e7i		−	0.140095i
$586$		0			0
$587$	2.86519e6	−	2.86519e6i	0.0141657	−	0.0141657i	−0.699988	−	0.714154i	$-0.746812\pi$
$587$	2.86519e6	−	2.86519e6i	0.0141657	−	0.0141657i	0.714154	+	0.699988i	$0.246812\pi$
$588$		0			0
$589$	3.47016e8	−	3.47016e8i	1.69826	−	1.69826i
$590$		0			0
$591$		−	1.10591e8i		−	0.535743i
$592$		0			0
$593$	7.90158e7			0.378922			0.189461	−	0.981888i	$-0.439326\pi$
$593$	7.90158e7			0.378922			0.189461	+	0.981888i	$0.439326\pi$
$594$		0			0
$595$	4.57311e7	+	4.57311e7i	0.217101	+	0.217101i
$596$		0			0
$597$	4.30119e7	+	4.30119e7i	0.202146	+	0.202146i
$598$		0			0
$599$	−3.85910e8			−1.79558			−0.897792	−	0.440419i	$-0.854830\pi$
$599$	−3.85910e8			−1.79558			−0.897792	+	0.440419i	$0.854830\pi$
$600$		0			0
$601$			2.00376e8i			0.923044i	0.887129	+	0.461522i	$0.152697\pi$
$601$			2.00376e8i			0.923044i	−0.887129	+	0.461522i	$0.847303\pi$
$602$		0			0
$603$	−1.84245e7	+	1.84245e7i	−0.0840320	+	0.0840320i
$604$		0			0
$605$	3.16968e8	−	3.16968e8i	1.43136	−	1.43136i
$606$		0			0
$607$		−	1.61943e7i		−	0.0724094i	−0.999344	−	0.0362047i	$-0.988473\pi$
$607$		−	1.61943e7i		−	0.0724094i	0.999344	−	0.0362047i	$-0.0115268\pi$
$608$		0			0
$609$	1.91799e8			0.849172
$610$		0			0
$611$	−3.56775e7	−	3.56775e7i	−0.156412	−	0.156412i
$612$		0			0
$613$	−1.23680e8	−	1.23680e8i	−0.536932	−	0.536932i	0.385695	−	0.922626i	$-0.373962\pi$
$613$	−1.23680e8	−	1.23680e8i	−0.536932	−	0.536932i	−0.922626	+	0.385695i	$0.873962\pi$
$614$		0			0
$615$	−1.64752e8			−0.708282
$616$		0			0
$617$			9.47161e7i			0.403244i	0.979463	+	0.201622i	$0.0646213\pi$
$617$			9.47161e7i			0.403244i	−0.979463	+	0.201622i	$0.935379\pi$
$618$		0			0
$619$	9.92581e7	−	9.92581e7i	0.418499	−	0.418499i	−0.466187	−	0.884686i	$-0.654373\pi$
$619$	9.92581e7	−	9.92581e7i	0.418499	−	0.418499i	0.884686	+	0.466187i	$0.154373\pi$
$620$		0			0
$621$	−4.00881e7	+	4.00881e7i	−0.167394	+	0.167394i
$622$		0			0
$623$		−	2.98408e8i		−	1.23409i
$624$		0			0
$625$	2.79165e8			1.14346
$626$		0			0
$627$	−2.33417e8	−	2.33417e8i	−0.946955	−	0.946955i
$628$		0			0
$629$	−1.57948e7	−	1.57948e7i	−0.0634690	−	0.0634690i
$630$		0			0
$631$	1.48727e8			0.591975			0.295987	−	0.955192i	$-0.404351\pi$
$631$	1.48727e8			0.591975			0.295987	+	0.955192i	$0.404351\pi$
$632$		0			0
$633$		−	2.00793e8i		−	0.791659i
$634$		0			0
$635$	2.74495e8	−	2.74495e8i	1.07205	−	1.07205i
$636$		0			0
$637$	1.76784e6	−	1.76784e6i	0.00683950	−	0.00683950i
$638$		0			0
$639$			1.26540e8i			0.484981i
$640$		0			0
$641$	1.07227e8			0.407127			0.203564	−	0.979062i	$-0.434748\pi$
$641$	1.07227e8			0.407127			0.203564	+	0.979062i	$0.434748\pi$
$642$		0			0
$643$	−1.39954e8	−	1.39954e8i	−0.526444	−	0.526444i	0.393067	−	0.919510i	$-0.371414\pi$
$643$	−1.39954e8	−	1.39954e8i	−0.526444	−	0.526444i	−0.919510	+	0.393067i	$0.871414\pi$
$644$		0			0
$645$	−1.32882e8	−	1.32882e8i	−0.495208	−	0.495208i
$646$		0			0
$647$	−1.74204e8			−0.643198			−0.321599	−	0.946876i	$-0.604220\pi$
$647$	−1.74204e8			−0.643198			−0.321599	+	0.946876i	$0.604220\pi$
$648$		0			0
$649$			1.27889e8i			0.467842i
$650$		0			0
$651$	−1.95043e8	+	1.95043e8i	−0.706948	+	0.706948i
$652$		0			0
$653$	−2.12946e8	+	2.12946e8i	−0.764769	+	0.764769i	−0.977180	−	0.212411i	$-0.931868\pi$
$653$	−2.12946e8	+	2.12946e8i	−0.764769	+	0.764769i	0.212411	+	0.977180i	$0.431868\pi$
$654$		0			0
$655$		−	2.27337e8i		−	0.808997i
$656$		0			0
$657$	−8.50342e7			−0.299846
$658$		0			0
$659$	−1.00416e8	−	1.00416e8i	−0.350870	−	0.350870i	0.509563	−	0.860433i	$-0.329807\pi$
$659$	−1.00416e8	−	1.00416e8i	−0.350870	−	0.350870i	−0.860433	+	0.509563i	$0.829807\pi$
$660$		0			0
$661$	1.71149e8	+	1.71149e8i	0.592611	+	0.592611i	0.938336	−	0.345725i	$-0.112367\pi$
$661$	1.71149e8	+	1.71149e8i	0.592611	+	0.592611i	−0.345725	+	0.938336i	$0.612367\pi$
$662$		0			0
$663$	−1.87354e7			−0.0642869
$664$		0			0
$665$			4.30839e8i			1.46504i
$666$		0			0
$667$	−3.84449e8	+	3.84449e8i	−1.29557	+	1.29557i
$668$		0			0
$669$	−3.83454e7	+	3.83454e7i	−0.128066	+	0.128066i
$670$		0			0
$671$			2.16838e8i			0.717740i
$672$		0			0
$673$	−4.72365e8			−1.54965			−0.774823	−	0.632178i	$-0.782161\pi$
$673$	−4.72365e8			−1.54965			−0.774823	+	0.632178i	$0.782161\pi$
$674$		0			0
$675$	7.26539e6	+	7.26539e6i	0.0236237	+	0.0236237i
$676$		0			0
$677$	1.35510e8	+	1.35510e8i	0.436721	+	0.436721i	0.890907	−	0.454186i	$-0.150070\pi$
$677$	1.35510e8	+	1.35510e8i	0.436721	+	0.436721i	−0.454186	+	0.890907i	$0.650070\pi$
$678$		0			0
$679$	−1.57018e8			−0.501580
$680$		0			0
$681$			1.85069e8i			0.585992i
$682$		0			0
$683$	1.86498e8	−	1.86498e8i	0.585344	−	0.585344i	−0.351023	−	0.936367i	$-0.614166\pi$
$683$	1.86498e8	−	1.86498e8i	0.585344	−	0.585344i	0.936367	+	0.351023i	$0.114166\pi$
$684$		0			0
$685$	4.34881e8	−	4.34881e8i	1.35300	−	1.35300i
$686$		0			0
$687$			2.07249e8i			0.639178i
$688$		0			0
$689$	−5.49856e7			−0.168109
$690$		0			0
$691$	2.83368e8	+	2.83368e8i	0.858849	+	0.858849i	0.991203	−	0.132354i	$-0.0422535\pi$
$691$	2.83368e8	+	2.83368e8i	0.858849	+	0.858849i	−0.132354	+	0.991203i	$0.542254\pi$
$692$		0			0
$693$	1.31194e8	+	1.31194e8i	0.394196	+	0.394196i
$694$		0			0
$695$	6.65684e8			1.98296
$696$		0			0
$697$			1.10054e8i			0.325017i
$698$		0			0
$699$	1.36725e8	−	1.36725e8i	0.400328	−	0.400328i
$700$		0			0
$701$	2.30227e8	−	2.30227e8i	0.668347	−	0.668347i	−0.288986	−	0.957333i	$-0.593318\pi$
$701$	2.30227e8	−	2.30227e8i	0.668347	−	0.668347i	0.957333	+	0.288986i	$0.0933182\pi$
$702$		0			0
$703$		−	1.48805e8i		−	0.428303i
$704$		0			0
$705$	1.24959e8			0.356615
$706$		0			0
$707$	1.54996e8	+	1.54996e8i	0.438594	+	0.438594i
$708$		0			0
$709$	−4.24526e7	−	4.24526e7i	−0.119115	−	0.119115i	0.645037	−	0.764152i	$-0.276842\pi$
$709$	−4.24526e7	−	4.24526e7i	−0.119115	−	0.119115i	−0.764152	+	0.645037i	$0.776842\pi$
$710$		0			0
$711$	−1.41952e8			−0.394941
$712$		0			0
$713$		−	7.81902e8i		−	2.15717i
$714$		0			0
$715$	1.83983e8	−	1.83983e8i	0.503339	−	0.503339i
$716$		0			0
$717$	−3.73642e7	+	3.73642e7i	−0.101367	+	0.101367i
$718$		0			0
$719$			2.52511e8i			0.679351i	0.940543	+	0.339676i	$0.110317\pi$
$719$			2.52511e8i			0.679351i	−0.940543	+	0.339676i	$0.889683\pi$
$720$		0			0
$721$	5.05503e8			1.34871
$722$		0			0
$723$	8.54803e7	+	8.54803e7i	0.226178	+	0.226178i
$724$		0			0
$725$	6.96758e7	+	6.96758e7i	0.182839	+	0.182839i
$726$		0			0
$727$	5.00217e8			1.30183			0.650916	−	0.759150i	$-0.274385\pi$
$727$	5.00217e8			1.30183			0.650916	+	0.759150i	$0.274385\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	−8.87646e7	+	8.87646e7i	−0.227241	+	0.227241i
$732$		0			0
$733$	−3.76387e8	+	3.76387e8i	−0.955703	+	0.955703i	−0.999060	−	0.0433569i	$-0.986195\pi$
$733$	−3.76387e8	+	3.76387e8i	−0.955703	+	0.955703i	0.0433569	+	0.999060i	$0.486195\pi$
$734$		0			0
$735$			6.19179e6i			0.0155939i
$736$		0			0
$737$	−2.41721e8			−0.603826
$738$		0			0
$739$	−1.52550e8	−	1.52550e8i	−0.377989	−	0.377989i	0.492387	−	0.870376i	$-0.336124\pi$
$739$	−1.52550e8	−	1.52550e8i	−0.377989	−	0.377989i	−0.870376	+	0.492387i	$0.836124\pi$
$740$		0			0
$741$	−8.82544e7	−	8.82544e7i	−0.216911	−	0.216911i
$742$		0			0
$743$	5.90150e8			1.43878			0.719392	−	0.694604i	$-0.244420\pi$
$743$	5.90150e8			1.43878			0.719392	+	0.694604i	$0.244420\pi$
$744$		0			0
$745$		−	2.19109e8i		−	0.529897i
$746$		0			0
$747$	1.83544e7	−	1.83544e7i	0.0440330	−	0.0440330i
$748$		0			0
$749$	−5.47887e8	+	5.47887e8i	−1.30390	+	1.30390i
$750$		0			0
$751$			9.72140e7i			0.229514i	0.993394	+	0.114757i	$0.0366089\pi$
$751$			9.72140e7i			0.229514i	−0.993394	+	0.114757i	$0.963391\pi$
$752$		0			0
$753$	−1.47992e8			−0.346620
$754$		0			0
$755$	1.97904e8	+	1.97904e8i	0.459847	+	0.459847i
$756$		0			0
$757$	9.05372e7	+	9.05372e7i	0.208708	+	0.208708i	0.803718	−	0.595010i	$-0.202852\pi$
$757$	9.05372e7	+	9.05372e7i	0.208708	+	0.208708i	−0.595010	+	0.803718i	$0.702852\pi$
$758$		0			0
$759$	−5.25937e8			−1.20284
$760$		0			0
$761$		−	1.81374e8i		−	0.411549i	−0.978599	−	0.205774i	$-0.934029\pi$
$761$		−	1.81374e8i		−	0.411549i	0.978599	−	0.205774i	$-0.0659713\pi$
$762$		0			0
$763$	−7.20085e7	+	7.20085e7i	−0.162110	+	0.162110i
$764$		0			0
$765$	3.28100e7	−	3.28100e7i	0.0732862	−	0.0732862i
$766$		0			0
$767$			4.83546e7i			0.107165i
$768$		0			0
$769$	3.12737e8			0.687701			0.343851	−	0.939024i	$-0.388269\pi$
$769$	3.12737e8			0.687701			0.343851	+	0.939024i	$0.388269\pi$
$770$		0			0
$771$	1.96403e8	+	1.96403e8i	0.428533	+	0.428533i
$772$		0			0
$773$	−5.33319e8	−	5.33319e8i	−1.15464	−	1.15464i	−0.985610	−	0.169035i	$-0.945935\pi$
$773$	−5.33319e8	−	5.33319e8i	−1.15464	−	1.15464i	−0.169035	−	0.985610i	$-0.554065\pi$
$774$		0			0
$775$	−1.41708e8			−0.304432
$776$		0			0
$777$			8.36368e7i			0.178293i
$778$		0			0
$779$	−5.18415e8	+	5.18415e8i	−1.09664	+	1.09664i
$780$		0			0
$781$	−8.30072e8	+	8.30072e8i	−1.74246	+	1.74246i
$782$		0			0
$783$		−	1.37608e8i		−	0.286653i
$784$		0			0
$785$	1.90443e8			0.393691
$786$		0			0
$787$	−2.52168e7	−	2.52168e7i	−0.0517328	−	0.0517328i	0.680767	−	0.732500i	$-0.261647\pi$
$787$	−2.52168e7	−	2.52168e7i	−0.0517328	−	0.0517328i	−0.732500	+	0.680767i	$0.761647\pi$
$788$		0			0
$789$	1.40236e8	+	1.40236e8i	0.285515	+	0.285515i
$790$		0			0
$791$	−4.17726e8			−0.844037
$792$		0			0
$793$			8.19859e7i			0.164407i
$794$		0			0
$795$	9.62925e7	−	9.62925e7i	0.191642	−	0.191642i
$796$		0			0
$797$	2.19556e7	−	2.19556e7i	0.0433682	−	0.0433682i	−0.685090	−	0.728458i	$-0.740237\pi$
$797$	2.19556e7	−	2.19556e7i	0.0433682	−	0.0433682i	0.728458	+	0.685090i	$0.240237\pi$
$798$		0			0
$799$		−	8.34719e7i		−	0.163644i
$800$		0			0
$801$	−2.14094e8			−0.416589
$802$		0			0
$803$	−5.57805e8	−	5.57805e8i	−1.07730	−	1.07730i
$804$		0			0
$805$	4.85386e8	+	4.85386e8i	0.930464	+	0.930464i
$806$		0			0
$807$	3.90755e8			0.743505
$808$		0			0
$809$		−	4.91857e7i		−	0.0928951i	−0.998921	−	0.0464476i	$-0.985210\pi$
$809$		−	4.91857e7i		−	0.0928951i	0.998921	−	0.0464476i	$-0.0147900\pi$
$810$		0			0
$811$	−1.05349e8	+	1.05349e8i	−0.197501	+	0.197501i	−0.798928	−	0.601427i	$-0.794599\pi$
$811$	−1.05349e8	+	1.05349e8i	−0.197501	+	0.197501i	0.601427	+	0.798928i	$0.294599\pi$
$812$		0			0
$813$	−4.45259e7	+	4.45259e7i	−0.0828592	+	0.0828592i
$814$		0			0
$815$		−	9.13510e7i		−	0.168749i
$816$		0			0
$817$	−8.36264e8			−1.53348
$818$		0			0
$819$	4.96040e7	+	4.96040e7i	0.0902953	+	0.0902953i
$820$		0			0
$821$	1.42572e8	+	1.42572e8i	0.257635	+	0.257635i	0.824091	−	0.566457i	$-0.191686\pi$
$821$	1.42572e8	+	1.42572e8i	0.257635	+	0.257635i	−0.566457	+	0.824091i	$0.691686\pi$
$822$		0			0
$823$	−8.79812e8			−1.57830			−0.789152	−	0.614199i	$-0.789479\pi$
$823$	−8.79812e8			−1.57830			−0.789152	+	0.614199i	$0.789479\pi$
$824$		0			0
$825$			9.53184e7i			0.169752i
$826$		0			0
$827$	−2.06154e8	+	2.06154e8i	−0.364481	+	0.364481i	−0.865460	−	0.500979i	$-0.832973\pi$
$827$	−2.06154e8	+	2.06154e8i	−0.364481	+	0.364481i	0.500979	+	0.865460i	$0.332973\pi$
$828$		0			0
$829$	2.98660e7	−	2.98660e7i	0.0524219	−	0.0524219i	−0.680410	−	0.732832i	$-0.738198\pi$
$829$	2.98660e7	−	2.98660e7i	0.0524219	−	0.0524219i	0.732832	+	0.680410i	$0.238198\pi$
$830$		0			0
$831$			5.98884e7i			0.104361i
$832$		0			0
$833$	4.13608e6			0.00715573
$834$		0			0
$835$	−5.42893e7	−	5.42893e7i	−0.0932512	−	0.0932512i
$836$		0			0
$837$	1.39935e8	+	1.39935e8i	0.238643	+	0.238643i
$838$		0			0
$839$	7.67224e8			1.29908			0.649541	−	0.760327i	$-0.274961\pi$
$839$	7.67224e8			1.29908			0.649541	+	0.760327i	$0.274961\pi$
$840$		0			0
$841$		−	7.24847e8i		−	1.21859i
$842$		0			0
$843$	3.31378e7	−	3.31378e7i	0.0553147	−	0.0553147i
$844$		0			0
$845$	−3.92620e8	+	3.92620e8i	−0.650732	+	0.650732i
$846$		0			0
$847$			1.12117e9i			1.84511i
$848$		0			0
$849$	1.55220e8			0.253644
$850$		0			0
$851$	−1.67644e8	−	1.67644e8i	−0.272020	−	0.272020i
$852$		0			0
$853$	−8.60861e8	−	8.60861e8i	−1.38703	−	1.38703i	−0.831489	−	0.555542i	$-0.812511\pi$
$853$	−8.60861e8	−	8.60861e8i	−1.38703	−	1.38703i	−0.555542	−	0.831489i	$-0.687489\pi$
$854$		0			0
$855$	3.09108e8			0.494552
$856$		0			0
$857$		−	5.10264e8i		−	0.810685i	−0.914165	−	0.405343i	$-0.867152\pi$
$857$		−	5.10264e8i		−	0.810685i	0.914165	−	0.405343i	$-0.132848\pi$
$858$		0			0
$859$	−2.06652e8	+	2.06652e8i	−0.326032	+	0.326032i	−0.851076	−	0.525043i	$-0.824049\pi$
$859$	−2.06652e8	+	2.06652e8i	−0.326032	+	0.326032i	0.525043	+	0.851076i	$0.324049\pi$
$860$		0			0
$861$	2.91379e8	−	2.91379e8i	0.456509	−	0.456509i
$862$		0			0
$863$		−	1.09999e9i		−	1.71142i	−0.517456	−	0.855710i	$-0.673121\pi$
$863$		−	1.09999e9i		−	1.71142i	0.517456	−	0.855710i	$-0.326879\pi$
$864$		0			0
$865$	−1.16233e9			−1.79589
$866$		0			0
$867$	2.44144e8	+	2.44144e8i	0.374619	+	0.374619i
$868$		0			0
$869$	−9.31171e8	−	9.31171e8i	−1.41896	−	1.41896i
$870$		0			0
$871$	−9.13943e7			−0.138314
$872$		0			0
$873$			1.12653e8i			0.169317i
$874$		0			0
$875$	−4.18772e8	+	4.18772e8i	−0.625106	+	0.625106i
$876$		0			0
$877$	−9.87963e7	+	9.87963e7i	−0.146468	+	0.146468i	−0.776538	−	0.630070i	$-0.783026\pi$
$877$	−9.87963e7	+	9.87963e7i	−0.146468	+	0.146468i	0.630070	+	0.776538i	$0.283026\pi$
$878$		0			0
$879$		−	2.40685e7i		−	0.0354390i
$880$		0			0
$881$	7.70267e8			1.12645			0.563227	−	0.826302i	$-0.309560\pi$
$881$	7.70267e8			1.12645			0.563227	+	0.826302i	$0.309560\pi$
$882$		0			0
$883$	8.65914e8	+	8.65914e8i	1.25775	+	1.25775i	0.952167	+	0.305578i	$0.0988497\pi$
$883$	8.65914e8	+	8.65914e8i	1.25775	+	1.25775i	0.305578	+	0.952167i	$0.401150\pi$
$884$		0			0
$885$	−8.46802e7	−	8.46802e7i	−0.122166	−	0.122166i
$886$		0			0
$887$	4.32770e8			0.620136			0.310068	−	0.950714i	$-0.399648\pi$
$887$	4.32770e8			0.620136			0.310068	+	0.950714i	$0.399648\pi$
$888$		0			0
$889$			9.70939e8i			1.38193i
$890$		0			0
$891$	9.41254e7	−	9.41254e7i	0.133068	−	0.133068i
$892$		0			0
$893$	3.93200e8	−	3.93200e8i	0.552153	−	0.552153i
$894$		0			0
$895$		−	1.17375e9i		−	1.63722i
$896$		0			0
$897$	−1.98856e8			−0.275525
$898$		0			0
$899$	1.34199e9	+	1.34199e9i	1.84701	+	1.84701i
$900$		0			0
$901$	−6.43228e7	−	6.43228e7i	−0.0879409	−	0.0879409i
$902$		0			0
$903$	4.70028e8			0.638353
$904$		0			0
$905$			7.15695e8i			0.965567i
$906$		0			0
$907$	1.78126e8	−	1.78126e8i	0.238729	−	0.238729i	−0.577595	−	0.816324i	$-0.696009\pi$
$907$	1.78126e8	−	1.78126e8i	0.238729	−	0.238729i	0.816324	+	0.577595i	$0.196009\pi$
$908$		0			0
$909$	1.11203e8	−	1.11203e8i	0.148055	−	0.148055i
$910$		0			0
$911$			1.02858e9i			1.36045i	0.733002	+	0.680226i	$0.238118\pi$
$911$			1.02858e9i			1.36045i	−0.733002	+	0.680226i	$0.761882\pi$
$912$		0			0
$913$	2.40801e8			0.316407
$914$		0			0
$915$	−1.43576e8	−	1.43576e8i	−0.187422	−	0.187422i
$916$		0			0
$917$	4.02066e8	+	4.02066e8i	0.521422	+	0.521422i
$918$		0			0
$919$	−6.52230e7			−0.0840339			−0.0420169	−	0.999117i	$-0.513378\pi$
$919$	−6.52230e7			−0.0840339			−0.0420169	+	0.999117i	$0.513378\pi$
$920$		0			0
$921$		−	7.39788e8i		−	0.946953i
$922$		0			0
$923$	−3.13849e8	+	3.13849e8i	−0.399131	+	0.399131i
$924$		0			0
$925$	−3.03831e7	+	3.03831e7i	−0.0383890	+	0.0383890i
$926$		0			0
$927$		−	3.62676e8i		−	0.455281i
$928$		0			0
$929$	−7.88148e8			−0.983016			−0.491508	−	0.870873i	$-0.663554\pi$
$929$	−7.88148e8			−0.983016			−0.491508	+	0.870873i	$0.663554\pi$
$930$		0			0
$931$	1.94833e7	+	1.94833e7i	0.0241442	+	0.0241442i
$932$		0			0
$933$	−7.99193e7	−	7.99193e7i	−0.0984027	−	0.0984027i
$934$		0			0
$935$	4.30452e8			0.526611
$936$		0			0
$937$			5.31183e8i			0.645692i	0.946451	+	0.322846i	$0.104640\pi$
$937$			5.31183e8i			0.645692i	−0.946451	+	0.322846i	$0.895360\pi$
$938$		0			0
$939$	−6.46069e7	+	6.46069e7i	−0.0780337	+	0.0780337i
$940$		0			0
$941$	−1.68586e8	+	1.68586e8i	−0.202327	+	0.202327i	−0.800996	−	0.598670i	$-0.795696\pi$
$941$	−1.68586e8	+	1.68586e8i	−0.202327	+	0.202327i	0.598670	+	0.800996i	$0.295696\pi$
$942$		0			0
$943$			1.16810e9i			1.39298i
$944$		0			0
$945$	−1.73736e8			−0.205871
$946$		0			0
$947$	−1.02795e8	−	1.02795e8i	−0.121039	−	0.121039i	0.643993	−	0.765031i	$-0.277277\pi$
$947$	−1.02795e8	−	1.02795e8i	−0.121039	−	0.121039i	−0.765031	+	0.643993i	$0.777277\pi$
$948$		0			0
$949$	−2.10905e8	−	2.10905e8i	−0.246768	−	0.246768i
$950$		0			0
$951$	3.13479e8			0.364475
$952$		0			0
$953$			9.78404e8i			1.13042i	0.824947	+	0.565210i	$0.191205\pi$
$953$			9.78404e8i			1.13042i	−0.824947	+	0.565210i	$0.808795\pi$
$954$		0			0
$955$	7.16661e8	−	7.16661e8i	0.822818	−	0.822818i
$956$		0			0
$957$	9.02673e8	−	9.02673e8i	1.02990	−	1.02990i
$958$		0			0
$959$			1.53825e9i			1.74410i
$960$		0			0
$961$	−1.84186e9			−2.07533
$962$		0			0
$963$	3.93084e8	+	3.93084e8i	0.440156	+	0.440156i
$964$		0			0
$965$	1.76778e8	+	1.76778e8i	0.196719	+	0.196719i
$966$		0			0
$967$	−7.24279e8			−0.800989			−0.400495	−	0.916299i	$-0.631162\pi$
$967$	−7.24279e8			−0.800989			−0.400495	+	0.916299i	$0.631162\pi$
$968$		0			0
$969$		−	2.06482e8i		−	0.226940i
$970$		0			0
$971$	2.79870e6	−	2.79870e6i	0.00305702	−	0.00305702i	−0.705577	−	0.708634i	$-0.749312\pi$
$971$	2.79870e6	−	2.79870e6i	0.00305702	−	0.00305702i	0.708634	+	0.705577i	$0.249312\pi$
$972$		0			0
$973$	−1.17732e9	+	1.17732e9i	−1.27807	+	1.27807i
$974$		0			0
$975$			3.60397e7i			0.0388837i
$976$		0			0
$977$	8.62168e8			0.924503			0.462252	−	0.886749i	$-0.347042\pi$
$977$	8.62168e8			0.924503			0.462252	+	0.886749i	$0.347042\pi$
$978$		0			0
$979$	−1.40441e9	−	1.40441e9i	−1.49674	−	1.49674i
$980$		0			0
$981$	5.16629e7	+	5.16629e7i	0.0547232	+	0.0547232i
$982$		0			0
$983$	−6.29606e8			−0.662839			−0.331419	−	0.943484i	$-0.607528\pi$
$983$	−6.29606e8			−0.662839			−0.331419	+	0.943484i	$0.607528\pi$
$984$		0			0
$985$			9.60696e8i			1.00526i
$986$		0			0
$987$	−2.21001e8	+	2.21001e8i	−0.229849	+	0.229849i
$988$		0			0
$989$	−9.42140e8	+	9.42140e8i	−0.973927	+	0.973927i
$990$		0			0
$991$			1.51486e9i			1.55651i	0.627947	+	0.778256i	$0.283895\pi$
$991$			1.51486e9i			1.55651i	−0.627947	+	0.778256i	$0.716105\pi$
$992$		0			0
$993$	−1.00473e9			−1.02613
$994$		0			0
$995$	−3.73642e8	−	3.73642e8i	−0.379303	−	0.379303i
$996$		0			0
$997$	−8.68297e7	−	8.68297e7i	−0.0876159	−	0.0876159i	0.661940	−	0.749556i	$-0.269733\pi$
$997$	−8.68297e7	−	8.68297e7i	−0.0876159	−	0.0876159i	−0.749556	+	0.661940i	$0.769733\pi$
$998$		0			0
$999$	6.00057e7			0.0601860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.a.31.9		48
4.3	odd	2		384.7.l.b.31.16		48
8.3	odd	2		48.7.l.a.43.17	yes	48
8.5	even	2		192.7.l.a.79.16		48
16.3	odd	4	inner	384.7.l.a.223.9		48
16.5	even	4		48.7.l.a.19.17	✓	48
16.11	odd	4		192.7.l.a.175.16		48
16.13	even	4		384.7.l.b.223.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.17	✓	48	16.5	even	4
48.7.l.a.43.17	yes	48	8.3	odd	2
192.7.l.a.79.16		48	8.5	even	2
192.7.l.a.175.16		48	16.11	odd	4
384.7.l.a.31.9		48	1.1	even	1	trivial
384.7.l.a.223.9		48	16.3	odd	4	inner
384.7.l.b.31.16		48	4.3	odd	2
384.7.l.b.223.16		48	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	384.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-11.0227 - 11.0227i) q^{3} +(95.7535 + 95.7535i) q^{5} -338.697 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(-11.0227 - 11.0227i) q^{3} +(95.7535 + 95.7535i) q^{5} -338.697 q^{7} +243.000i q^{9} +(-1594.02 + 1594.02i) q^{11} +(-602.697 + 602.697i) q^{13} -2110.92i q^{15} -1410.09 q^{17} +(-6642.31 - 6642.31i) q^{19} +(3733.36 + 3733.36i) q^{21} -14966.5 q^{23} +2712.47i q^{25} +(2678.52 - 2678.52i) q^{27} +(25687.3 - 25687.3i) q^{29} +52243.3i q^{31} +35140.9 q^{33} +(-32431.4 - 32431.4i) q^{35} +(11201.3 + 11201.3i) q^{37} +13286.7 q^{39} -78047.4i q^{41} +(62949.8 - 62949.8i) q^{43} +(-23268.1 + 23268.1i) q^{45} +59196.3i q^{47} -2933.21 q^{49} +(15543.0 + 15543.0i) q^{51} +(45616.2 + 45616.2i) q^{53} -305266. q^{55} +146432. i q^{57} +(40115.2 - 40115.2i) q^{59} +(68015.9 - 68015.9i) q^{61} -82303.4i q^{63} -115421. q^{65} +(75821.1 + 75821.1i) q^{67} +(164972. + 164972. i) q^{69} +520740. q^{71} +349935. i q^{73} +(29898.7 - 29898.7i) q^{75} +(539891. - 539891. i) q^{77} +584164. i q^{79} -59049.0 q^{81} +(-75532.5 - 75532.5i) q^{83} +(-135021. - 135021. i) q^{85} -566286. q^{87} +881047. i q^{89} +(204132. - 204132. i) q^{91} +(575863. - 575863. i) q^{93} -1.27205e6i q^{95} +463594. q^{97} +(-387347. - 387347. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 2720 q^{11} - 3936 q^{19} - 26240 q^{23} - 66400 q^{29} + 162336 q^{35} + 7200 q^{37} + 340704 q^{43} + 806736 q^{49} + 80352 q^{51} - 443680 q^{53} - 232704 q^{55} - 886144 q^{59} + 326496 q^{61} - 372832 q^{65} - 962112 q^{67} - 541728 q^{69} - 534016 q^{71} - 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} - 2497760 q^{83} + 372000 q^{85} + 775008 q^{91} - 660960 q^{99}+O(q^{100}) \) 48 * q - 2720 * q^11 - 3936 * q^19 - 26240 * q^23 - 66400 * q^29 + 162336 * q^35 + 7200 * q^37 + 340704 * q^43 + 806736 * q^49 + 80352 * q^51 - 443680 * q^53 - 232704 * q^55 - 886144 * q^59 + 326496 * q^61 - 372832 * q^65 - 962112 * q^67 - 541728 * q^69 - 534016 * q^71 - 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 - 2497760 * q^83 + 372000 * q^85 + 775008 * q^91 - 660960 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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